Mathematics and philosophy of mathematics

Philosophia Mathematica 2 (2):148-160 (1994)
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Abstract

The purpose of this note is to examine the relationship between the practice of mathematics and the philosophy of mathematics, ontology in particular. One conclusion is that the enterprises are (or should be) closely related, with neither one dominating the other. One cannot 'read off' the correct way to do mathematics from the true ontology, for example, nor can one ‘read off’ the true ontology from mathematics as practiced.

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10.1093/philmat/2.2.148

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Stewart Shapiro
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Citations of this work

Set theoretic naturalism.Penelope Maddy - 1996 - Journal of Symbolic Logic 61 (2):490-514.
Phenomenology and mathematical practice.Mary Leng - 2002 - Philosophia Mathematica 10 (1):3-14.

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References found in this work

Empiricism, Semantics and Ontology.Rudolf Carnap - 1950 - Revue Internationale de Philosophie 4 (11):20-40.
Anti-realism and logic: truth as eternal.Neil Tennant - 1987 - New York: Oxford University Press.
Russell's Mathematical Logic.Kurt Gödel - 1946 - In Paul Arthur Schilpp (ed.), The Philosophy of Bertrand Russell, 2nd edition. Evanston, IL: The Library of Living Philosophers, Inc.. pp. 123-154.
Informal Rigour and Completeness Proofs.Georg Kreisel - 1967 - In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. North-Holland. pp. 138--157.

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